Energy Function Approach Research Articles

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Iterative Learning Control of Constrained Systems With Varying Trial Lengths Under Alignment Condition.

This brief is concerned with iterative learning control (ILC) of constrained multi-input multi-output (MIMO) nonlinear systems under the state alignment condition with varying trial lengths. A modified reference trajectory is constructed to meet the alignment condition by adjusting the reference trajectory to be spatially closed. Resorting to the barrier composite energy function (BCEF) approach, an adaptive ILC scheme is built to guarantee the bounded convergence of the resultant closed-loop system. Illustrative examples are presented to verify the validity of the proposed iteration scheme.

Robust Iterative Learning Control for Pneumatic Muscle With Uncertainties and State Constraints

In this article, we propose a new iterative learning control (ILC) scheme for trajectory tracking of pneumatic muscle (PM) actuators with state constraints. A PM model is constructed in three-element form with both parametric and nonparametric uncertainties, while full state constraints are considered for enhancing operational safety. To ensure that system states are within the predefined bounds, the barrier Lyapunov function (BLF) is used in the analysis, which reaches infinity when some of its arguments approach limits. The proposed ILC incorporates the BLF with the composite energy function (CEF) approach and ensures the boundedness of CEF in the closed-loop, thus, assuring that those limits are not transgressed. Through rigorous analysis, we show that under the proposed ILC scheme, uniform convergences of PM state tracking errors are guaranteed. Simulation studies and experimental validations are conducted to illustrate the efficacy of the proposed scheme. Experimental results show that the proposed ILC satisfies the state constraint requirements and the tracking error is less than 2.5% of the desired trajectory.

Engineered Interphase Mechanics in Single Lap Joints: Analytical and PINN Formulations

Adhesively bonded joints showcase non-uniform stress distribution, along their length as the load is transferred through layers of dissimilar stiffness. For efficient transfer of loads, the peak interfacial shear stress is required to be engineered. In this study, inspired by electric pulses, the interphase modulus is modified according to square, sinusoidal and triangular pulses. The variation in peak stresses with increased number of pulses up to four is also investigated. The developed analytical model is solved for the interfacial shear stresses as well as the peel stresses, using energy functional approach, through MAPLE software. The abrupt changes in modulus in square pulse graded interphase are observed to create highest interfacial shear stresses among the considered grading profiles. Furthermore, the peak interfacial stresses are observed to increase with increased number of pulses. An effective elastic modulus parameter is defined to indicate the area under the modulus profile curve. The effective modulus is found to be gradually increasing with increase number of pulses in square graded interphase. Whereas, it is constant for sinusoidal- and triangular-graded interphases. A deep machine learning-based physics informed neural network model is developed to quickly solve the developed governing differential equations. Therefore, results from the machine leaning model are compared to the analytical results.

Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

In materials with strong electron-phonon ($e$-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons [N.-E. Lee et al., Phys. Rev. Mater. 5, 063805 (2021)]. A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature [W. H. Sio et al., Phys. Rev. Lett. 122, 246403 (2019); Phys. Rev. B 99, 235139 (2019)]. In this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here, it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

Stable Steady-State Solutions of Some Biological Aggregation Models

Aggregation phenomena occur across the biological sciences, from cell adhesion to insect swarms, animal home ranges to human cities. Understanding the mechanisms by which they may spontaneously emerge has therefore generated much interest from applied mathematicians. Partial differential equations (PDEs) with nonlocal advection offer a popular formalism for studying aggregations. However, the inherent nonlocality, often necessary for ensuring continuum models are well-posed, makes their study technically challenging. Here, we take a different approach by studying a discrete-space system that can be formally related to classical nonlocal PDE approaches via a limiting procedure. We show how to find expressions for the asymptotically stable steady-states of this discrete-space system via an energy functional approach. This allows us to predict the size of aggregations as a function of the underlying movement mechanisms of individual organisms. We apply this to a recent model of cell adhesion, revealing a hysteresis property whereby the existing aggregations may persist even as the adhesion tendency decreases past the bifurcation point. We compare this to numerical solutions of the associated nonlocal PDE system, showing that the hysteresis property predicted by the discrete-space expressions is also present in the continuum system.

A novel RK4-Hopfield Neural Network for Power Flow Analysis of power system

This paper presents a novel Runge–Kutta (RK4) based modified hopfield neural network (MHNN) for solving a set of non-linear transcendental power flow equations of power system. The proffered method is a Lyapunov based energy function approach to minimize real and reactive power mismatches of the system. A set of non-linear differential equations derived from energy function, describing the dynamical behavior of HNN is framed for solving Power Flow equations. These dynamic equations of the network are solved by RK4 method to deduce the unknown variables of the system. The feasibility of proposed method is tested on 5-bus, IEEE 14-bus, 39-bus and 57-bus test system. The analytical equation describing the behavior of MHNN is coded in MATLAB software. The results obtained reveal that the suggested method gives accurate solution and reduces the computational complexity than conventional Newton Raphson (NR) method. The sensitivity analysis is also tested for change in R/X ratio of the system, initial conditions and loading of the system. The proposed method is robust for above specified changes and involves less computational effort. To prove the applicability and consistency of projected method, IEEE 118-bus system has been tested. The power flow solutions found through proffered method are compared with solutions obtained from numerical approaches in order to validate the proposed approach. Moreover, the stability of the system is studied in Lyapunov sense of notion which assures converged solution of proposed method.

Least‐cost generation expansion planning using whale optimization algorithm incorporating emission reduction and renewable energy sources

Ever-increasing energy demand and technology development are continuously pursuing the attention of power system planners to design an optimum strategy for supplying future electrical demand. Generation expansion planning turns out to be a crucial step for an efficient energy management system in a modern power grid. In this paper, a novel whale optimization algorithm with penalty factor approach (WOA-PFA) framework has been developed to solve a nonlinear, discrete, dynamic, highly complex, heavily constrained GEP problem. Reliability evaluation is accomplished using equivalent energy function approach. A virtual mapping procedure is utilized to add computational strength to the WOA-PFA framework. Emission reduction is performed by utilizing total emission reduction constraint. The results are organized in four case studies starting with base power plants and adding wind, solar, and solar with storage facility in succession for the rest of case studies. Simulation results prove that the proposed WOA-PFA shows promising results in terms of the least cost and computational time as compared with the techniques presented in the literature.

Integrations of Neural Networks and Transient Energy Functions for Designing Supplementary Damping Control of UPFC

This article presents an integrated scheme for supplementary damping control of unified power flow controllers (UPFCs) in order to mitigate low-frequency oscillations in power systems. The entire control system consists of the primary control and the supplementary control. In the primary control, the passivity-based control is considered in the current control loop of two converters for achieving more prompt and accurate dynamical responses. In the supplementary control, the transient energy function (TEF) approach will be explored first for designing the damping control of UPFCs. This control action can be considered as an extension of droop control used in the synchronous generator. In order to further cope with unmodeled dynamics of power systems and provide the online dynamic adaptation ability, neural networks approximated control actions are designated for online weight adjustments of the TEF-based supplementary control. Numerical simulations on three benchmark systems have been performed to validate the proposed control method for providing the extra damping and suppressing power swings even under severe operating conditions.

Power Flow Solvers for Direct Current Networks

With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This paper puts forth three approaches with complementary strengths towards coping with the PF task in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. The first approach relies on a monotone mapping. In the absence of constant-power generation, the related iterates converge to the high-voltage solution, if one exists. To handle generators operating in constant-power mode at any time, an alternative Z-bus method is studied. For bounded constant-power generation and demand, the analysis establishes the existence and uniqueness of a PF solution within a predefined ball. Moreover, the Z-bus updates converge to this solution. Third, an energy function approach shows that under limited constant-power demand, all PF solutions are local minima of a function. The derived conditions can be checked without knowing the system state. The applicability of the conditions and the performance of the algorithms are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.

Simultaneous multiple-parameter control in flexible power systems for its stability enhancement

In the paper, a practical and innovative approach for determining control parameters of multiple and/or multi-parametric controllable elements with the aim of handling electromechanical dynamic phenomena in a power system, is presented. For the sake of a clear representation, a Unified Power-Flow Controller (as some kind of a synonym for multi-parametric devices) is provided, even though the suggested idea may be easily extended to coordinated control of arbitrary number of other devices as well. Application of a power-system transient energy function enables the strategy to reach a global optimum in the Lyapunov sense. Setting of controlled damping-device parameters pursues minimization of the time derivative of the transient energy function, which corresponds to the fastest possible dissipation of the energy surplus, gained during a disturbance. This is achieved by putting into use its newly presented predictable relationship with the damping-device parameter setting. Optimality of the strategy was demonstrated on both the single-machine infinite-bus model as well as on the Slovenian power-system model for damping of reconstructed power oscillations. An additional important contribution of the strategy is its easy-to-implement feature within existing commercial power-system dynamic analysis software tools, as transient energy function approach normally requires special software solutions.

Multi-objective region reaching control for a swarm of robots

This paper is concerned with the multi-objective region reaching control for a swarm of robots which are formulated by Lagrangian dynamics. Two distributed multi-objective region reaching control protocols are proposed for the networked robotic systems under directed acyclic topology, and a unifying methodology is presented to perform the convergence analysis for the robotic systems with static and moving target regions. The control strategy is developed by using the potential energy function approach, and the specified shapes of the various desired regions are constructed by selecting appropriate objective functions. In this control strategy, a network of a large number of robots evolves into multiple groups, and the robots in each group only require communicating with their neighbors. Thus, the proposed control strategy is effective for multi-objective region reaching control for a swarm of robots in practical applications. Finally, simulation examples are given to show the validity of the theoretical results.,

Adaptive finite-time reconfiguration control of unmanned aerial vehicles with a moving leader

This paper investigates adaptive reconfiguration control problem for unmanned aerial vehicle (UAV) helicopter system with a moving leader. Only part of UAV helicopter is informed to have access to the leader’s position. The six degree-of-freedom UAV system is composed of position outer loop and attitude inner loop. In this paper, we introduce a new fully distributed, finite-time reconfiguration controller and the problem of inter-UAVs collision avoidance was solved using potential energy function approach, extending the asymptotical formation controller without collision avoidance from the literature. The distinctive feature of our algorithm from existing works is that the novel formation reconfiguration controller can achieve finite-time, collision avoidance and fully distributed formation only based on relative positions between UAV and its adjacents. It means that the control algorithm is independent of any global information that requires to be calculated by each follower UAV. The system uncertainties are estimated by radial basis function neural network in practical finite time. Simulation results are shown to demonstrate the efficiency of the designed strategy.

Consensus-Based Droop Control of Isolated Micro-Grids by ADMM Implementations

Due to low inertia, high penetration of renewable generators in isolated micro-grids may result in poor frequency and voltage response under large disturbances. In order to overcome this difficulty, the distributed average consensus algorithm has been studied recently by extending local droop control mechanisms of power converters into distributed droop control. However, its convergence rate and the resilience to noises are still not satisfactory. In this paper, two implementations of consensus-based distributed droop control by the alternating direction multipliers method are proposed. It can be shown that the closed-loop system is described by the second-order vector differential equation, and the stability of every trajectory can be analyzed by the energy function approach under certain mild conditions. Real-time digital simulations are performed to validate the effectiveness of the proposed distributed droop control mechanism.

Distributed learning consensus for heterogenous high-order nonlinear multi-agent systems with output constraints

This paper considers the learning consensus problem for heterogenous high-order nonlinear multi-agent systems with output constraints. The dynamics consisting of parameterized and lumped uncertainties is different among different agents. To solve the consensus problem under output constraints, two distributed control protocols are designed with the help of a novel barrier Lyapunov function, which drives the control updating and parameters learning. Both convergence analysis and constraint satisfaction are strictly proved by the barrier composite energy function approach. Illustrative simulations are provided to verify the effectiveness of the proposed protocols.

Fault Tolerant Nonrepetitive Trajectory Tracking for MIMO Output Constrained Nonlinear Systems Using Iterative Learning Control.

Most works on iterative learning control (ILC) assume identical reference trajectories for the system state over the iteration domain. This fundamental assumption may not always hold in practice, where the desired trajectories or control objectives may be iteration dependent. In this paper, we relax this fundamental assumption, by introducing a new way of modifying the reference trajectories. The concept of modifier functions has been introduced for the first time in the ILC literature. This proposed approach is also a unified framework that can handle other common types of initial conditions in ILC. Multi-input multi-output nonlinear systems are considered, which can be subject to the actuator faults. Time and iteration dependent constraint requirements on the system output can be effectively handled. Backstepping design and composite energy function approach are used in the analysis. We show that in the closed loop analysis, the proposed control scheme can guarantee uniform convergence on the full state tracking error over the iteration domain, beyond a small initial time interval in each iteration, while the constraint requirements on the system output are never violated. In the end two simulation examples are shown to illustrate the efficacy of the proposed ILC algorithm.

Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints

SummaryThis paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ‐type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively from both theoretical and practical viewpoints. These schemes include the original adaptive scheme, projection‐based scheme, smooth function‐based scheme and its alternative, and dead‐zone–like scheme. The consensus convergence and constraints guarantee are strictly proved for each control scheme by using the barrier composite energy function approach. Illustrative simulations verify the theoretical analysis.

An Open State Model of the Navab Channel Explored by Rosetta and Molecular Dynamics Simulation

Voltage-gated sodium (Nav) channels play a pivotal role in propagating electrical signals in excitable cells and key targets for development of novel therapeutics. Despite recent progress in determining x-ray structures of bacterial Nav channels in closed, inactivated, and partially open states, we are still missing a stable open state structure of a Nav channel that will be useful to study ion conduction, channel gating and drug - channel interactions. We used Rosetta molecular modeling software to build the full-length open state model of the bacterial NavAb channel. The fully activated state of the NavAb voltage sensor domain (VSD) was modeled using the crystal structure of NavRh channel VSD as a template. The initial open state of NavAb pore was modeled using the crystal structure of NavMs with partially open pore. Rebuilding the interacting regions of NavAb (S3, S4, S5, S6, and S4-S5 linker) using Rosetta loop modeling and relax approaches was essential to generate stable NavAb open state model. Output models were evaluated using RosettaMembrane energy function and Rosetta clustering approach. The top Rosetta models represented different alternative open states of the NavAb channel. We have conducted a set of molecular dynamics (MD) simulations on the NavAb channel open state model using the Anton supercomputer to examine its stability. The simulations revealed that the NavAb channel open state model reproducibly sustained a fully hydrated open pore that conducted sodium ions under an applied membrane potential for periods of hundreds of nanoseconds. These results suggest that our structural modeling approach could be useful for modeling multiple states of other ion channels and for rational design of novel therapeutics targeting ion channels.

Energy function applied to voltage stability studies – Discussion on low voltage solutions with the help of tangent vector

Two main topics regarding the energy function approach for voltage stability analysis are addressed in this paper. First, the problem of the critical low voltage solution identification is discussed. For this sake, the ability of the tangent vector method to correctly identify the low voltage solution that ultimately coalesce with the power system operating solution is investigated. It is shown that the methodology is consistent with the mechanism of the low voltage solutions. Second, the definition of the group of buses related to the weak area of a system is addressed. It is shown that the combined use of the low voltage solution methodology and the tangent vector technique yields good results. Tests were carried out in the IEEE-30, IEEE-57 and IEEE-118 bus test systems.

An effective mean field theory for the coexistence of anti-ferromagnetism and superconductivity: Applications to iron-based superconductors and cold Bose–Fermi atomic mixtures

We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose–Einstein condensation (BEC) in electronic systems and Bose–Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study a single effective model relevant for both systems within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.